The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 23 minutes of calls is $16.78, and the remaining credit after 54 minutes of calls is $12.44. What is the remaining credit after minutes of calls?

Step-by-step explanation:

let x represent the number of minutes of call.

Let y represent the remaining credit after x minutes of call.

If we plot y on the vertical axis and x on the horizontal axis, a straight line would be formed. The slope of the straight line would be

Slope, m = (12.44 - 16.78) / (54 - 23)

m = - 4.34/31 = - 0.14

The equation of the straight line can be represented in the slope-intercept form, y = mx + c

Where

c = intercept

m = slope

To determine the intercept, we would substitute x = 54, y = 12.44 and m = - 0.14 into y = mx + c. It becomes

12.44 = - 0.14 * 54 + c

12.44 = - 7.56 + c

c = 12.44 + 7.56

c = 20

The linear function becomes

y = - 0.14x + 20